TSTP Solution File: SYN033-1 by Twee---2.4.2
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% File : Twee---2.4.2
% Problem : SYN033-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 03:32:46 EDT 2023
% Result : Unsatisfiable 0.13s 0.35s
% Output : Proof 0.13s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SYN033-1 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.12 % Command : parallel-twee %s --tstp --conditional-encoding if --smaller --drop-non-horn --give-up-on-saturation --explain-encoding --formal-proof
% 0.13/0.32 % Computer : n009.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Sat Aug 26 17:43:05 EDT 2023
% 0.13/0.32 % CPUTime :
% 0.13/0.35 Command-line arguments: --flatten
% 0.13/0.35
% 0.13/0.35 % SZS status Unsatisfiable
% 0.13/0.35
% 0.13/0.36 % SZS output start Proof
% 0.13/0.36 Take the following subset of the input axioms:
% 0.13/0.36 fof(clause1, axiom, ![A, B]: p(g(A, B), A, B)).
% 0.13/0.36 fof(clause2, axiom, ![A3, B2]: p(A3, h(A3, B2), B2)).
% 0.13/0.36 fof(clause3, axiom, ![C, D, E, F, A2, B2]: (~p(A2, B2, C) | (~p(D, E, B2) | (~p(A2, D, F) | p(F, E, C))))).
% 0.13/0.36 fof(prove_something, negated_conjecture, ![A3]: ~p(k(A3), A3, k(A3))).
% 0.13/0.36
% 0.13/0.36 Now clausify the problem and encode Horn clauses using encoding 3 of
% 0.13/0.36 http://www.cse.chalmers.se/~nicsma/papers/horn.pdf.
% 0.13/0.36 We repeatedly replace C & s=t => u=v by the two clauses:
% 0.13/0.36 fresh(y, y, x1...xn) = u
% 0.13/0.36 C => fresh(s, t, x1...xn) = v
% 0.13/0.36 where fresh is a fresh function symbol and x1..xn are the free
% 0.13/0.36 variables of u and v.
% 0.13/0.36 A predicate p(X) is encoded as p(X)=true (this is sound, because the
% 0.13/0.36 input problem has no model of domain size 1).
% 0.13/0.36
% 0.13/0.36 The encoding turns the above axioms into the following unit equations and goals:
% 0.13/0.36
% 0.13/0.36 Axiom 1 (clause3): fresh3(X, X, Y, Z, W) = true2.
% 0.13/0.36 Axiom 2 (clause2): p(X, h(X, Y), Y) = true2.
% 0.13/0.36 Axiom 3 (clause1): p(g(X, Y), X, Y) = true2.
% 0.13/0.36 Axiom 4 (clause3): fresh(X, X, Y, Z, W, V, U) = p(U, V, W).
% 0.13/0.36 Axiom 5 (clause3): fresh2(X, X, Y, Z, W, V, U, T) = fresh3(p(Y, Z, W), true2, W, U, T).
% 0.13/0.36 Axiom 6 (clause3): fresh2(p(X, Y, Z), true2, W, Z, V, X, Y, U) = fresh(p(W, X, U), true2, W, Z, V, Y, U).
% 0.13/0.36
% 0.13/0.36 Goal 1 (prove_something): p(k(X), X, k(X)) = true2.
% 0.13/0.36 The goal is true when:
% 0.13/0.36 X = h(X, X)
% 0.13/0.36
% 0.13/0.36 Proof:
% 0.13/0.36 p(k(h(X, X)), h(X, X), k(h(X, X)))
% 0.13/0.36 = { by axiom 4 (clause3) R->L }
% 0.13/0.36 fresh(true2, true2, g(X, k(h(X, X))), X, k(h(X, X)), h(X, X), k(h(X, X)))
% 0.13/0.36 = { by axiom 3 (clause1) R->L }
% 0.13/0.36 fresh(p(g(X, k(h(X, X))), X, k(h(X, X))), true2, g(X, k(h(X, X))), X, k(h(X, X)), h(X, X), k(h(X, X)))
% 0.13/0.36 = { by axiom 6 (clause3) R->L }
% 0.13/0.36 fresh2(p(X, h(X, X), X), true2, g(X, k(h(X, X))), X, k(h(X, X)), X, h(X, X), k(h(X, X)))
% 0.13/0.36 = { by axiom 2 (clause2) }
% 0.13/0.36 fresh2(true2, true2, g(X, k(h(X, X))), X, k(h(X, X)), X, h(X, X), k(h(X, X)))
% 0.13/0.36 = { by axiom 5 (clause3) }
% 0.13/0.36 fresh3(p(g(X, k(h(X, X))), X, k(h(X, X))), true2, k(h(X, X)), h(X, X), k(h(X, X)))
% 0.13/0.36 = { by axiom 3 (clause1) }
% 0.13/0.36 fresh3(true2, true2, k(h(X, X)), h(X, X), k(h(X, X)))
% 0.13/0.36 = { by axiom 1 (clause3) }
% 0.13/0.36 true2
% 0.13/0.36 % SZS output end Proof
% 0.13/0.36
% 0.13/0.36 RESULT: Unsatisfiable (the axioms are contradictory).
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